arXiv:2607. 21199v1 Announce Type: cross Abstract: Grounding, the translation of high-level theories into equivalent quantifier-free formulas, is a crucial step in declarative solving, yet it has so far escaped the proof-logging revolution.
Grounding, the translation of high-level theories into equivalent quantifier-free formulas, is a crucial step in declarative solving, yet it has so far escaped the proof-logging revolution. When this grounding step is not certifying, there is no way of knowing that the obtained solutions actually correspond to the original problem specification, resulting in a trust gap.
The paper introduces a new calculus that integrates ground instantiations, CDCL(T)-style rules, and non‑ground conflict analysis for SMT solving. By performing resolution on the original non‑ground clauses, the solver learns more general, often non‑redundant clauses, potentially yielding exponentially shorter proofs. The approach also incorporates chronological backtracking and is shown to simulate several existing solving frameworks, including CDCL, SCL(FOL), SCL(T), and Resolution.
arXiv:2607. 13069v1 Announce Type: new Abstract: Large language models produce chain-of-thought (CoT) reasoning that appears logically sound yet may not genuinely depend on its stated premises.
arXiv:2608. 09190v1 Announce Type: new Abstract: GK is a query-directed first-order prover that extends ordinary resolution-based proof search with explicit positive and negative claims, numerical confidence values, and prioritized default rules with exceptions.
arXiv:2608. 19009v2 Announce Type: replace Abstract: Large language models (LLMs) are increasingly paired with verifiers (step checkers, self-consistency filters, tool-based fact checkers, formal proof assistants) that claim to detect the model's errors.
arXiv:2606. 00671v1 Announce Type: new Abstract: We present AXIOM, a trust-first neuro-symbolic execution architecture for natural-language mathematical reasoning.
arXiv:2603. 18334v2 Announce Type: replace-cross Abstract: As Large Language Models (LLMs) increasingly assist secure software development, their ability to meet the rigorous demands of Rust program verification remains unclear.
FaithSieve is a Lean‑assisted framework that fine‑grains natural‑language mathematical proofs into local reasoning units, extracts typed proof obligations, and verifies them with formal evidence gated by semantic alignment. It introduces two expert‑verified datasets—ProofLoc‑Olympiad and ProofLoc‑University—to benchmark first‑error localization. On these benchmarks, FaithSieve outperforms direct‑judging baselines, achieving 81.43% and 84.5% exact first‑error accuracy respectively.
The paper introduces GUARD, a neuro‑symbolic system that autoformalizes argumentative material by completing missing premises (guards) before formal verification. It uses large language models to generate candidate guards, Isabelle/HOL to verify them, and a contrastive test to ensure the proof depends on the original premises and does not over‑generalize. Experiments on Debatepedia and ARCT show that GUARD improves verified‑faithful scores by over 30 points and reduces leakage by about 20 points compared to prior LLM‑driven theorem proving methods.
arXiv:2609.36279v1 Announce Type: cross Abstract: The shallow embedding of higher-order modal logic in classical higher-order logic, used in Benzm\"uller and Scott's Notes on G\"odel's and Scott's va...
arXiv:2607. 16372v1 Announce Type: cross Abstract: Interactive theorem proving (ITP) underpins program verification and formalized mathematics, but its manual effort limits scalability.
arXiv:2606. 20227v1 Announce Type: new Abstract: Large Language Models (LLMs) have made significant progress in reasoning, particularly in deductive reasoning, which is crucial for high-stakes decision-making.